ChebConv

class dgl.nn.tensorflow.conv.ChebConv(*args, **kwargs)

Bases: tensorflow.python.keras.engine.base_layer.Layer

Chebyshev Spectral Graph Convolution layer from Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

\[ \begin{align}\begin{aligned}h_i^{l+1} &= \sum_{k=0}^{K-1} W^{k, l}z_i^{k, l}\\Z^{0, l} &= H^{l}\\Z^{1, l} &= \tilde{L} \cdot H^{l}\\Z^{k, l} &= 2 \cdot \tilde{L} \cdot Z^{k-1, l} - Z^{k-2, l}\\\tilde{L} &= 2\left(I - \tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2}\right)/\lambda_{max} - I\end{aligned}\end{align} \]

where \(\tilde{A}\) is \(A\) + \(I\), \(W\) is learnable weight.

Parameters

• in_feats (int) – Dimension of input features; i.e, the number of dimensions of \(h_i^{(l)}\).

• out_feats (int) – Dimension of output features \(h_i^{(l+1)}\).

• k (int) – Chebyshev filter size \(K\).

• activation (function, optional) – Activation function. Default ReLu.

• bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

Example

>>> import dgl
>>> import numpy as np
>>> import tensorflow as tf
>>> from dgl.nn import ChebConv
>>> with tf.device("CPU:0"):
...     g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
...     feat = tf.ones((6, 10))
...     conv = ChebConv(10, 2, 2)
...     res = conv(g, feat)
...     res
<tf.Tensor: shape=(6, 2), dtype=float32, numpy=
array([[ 0.6163, -0.1809],
        [ 0.6163, -0.1809],
        [ 0.6163, -0.1809],
        [ 0.9698, -1.5053],
        [ 0.3664,  0.7556],
        [-0.2370,  3.0164]], dtype=float32)>